# Conservation of momentum, KE

1. Jul 13, 2011

### cep

1. The problem statement, all variables and given/known data

Ball One: 0.4 kg, energy 100J before collision.
Ball Two: 0.6 kg, energy 112J before collision.

Two balls are thrown at each other and collide in midair. Ball Two flies off at an angle 32º below the horizontal with an energy of 95J. At what angle and speed did Ball One move away from the collision?

2. Relevant equations

Conservation of momentum, conservation of kinetic energy.

KE=1/2*m*v^2

3. The attempt at a solution

I have no idea how to find the angle of deflection, but I thought I could get the velocity of the ball as follows:

The total kinetic energy in the system should be conserved, so KE1i+KE2i = KE tot

KEtot-KE2f = KE1f = 1/2*m1*v1f^2

v1f = sqrt (2KE1f/m1) = sqrt (2*(222-95)/0.4) = 25.1 m/s

The answer in the back of the book is 20 m/s, 40º above the horizontal. Keep in mind, this is a first edition textbook, so answers are often incorrect. Any suggestions?

Thanks :)

2. Jul 13, 2011

### cep

No angle of collision is specified; the diagram in the book makes it look as though both balls are traveling along in the x-direction only.

3. Jul 14, 2011

### bacon

cep, I get an answer that is very close to your book, 21.4 m/s and 41.4 degrees.
I don't think you can assume conservation of kinetic energy. In my experience working these types of problems it needs to be stated a) that kinetic energy is conserved, or b) that the collision is "elastic", if you are to use the conservation of kinetic energy. You can do the problem using only the conservation of momentum and the definition of kinetic energy.
The momentum before the collision can be found using the masses given and the velocities calculated from the equation for kinetic energy for each mass. Of course this is along the x axis. The momentum along the y axis is zero.
After the collision, since momentum is conserved, the momentum along each axis must be the same as before the collision. The problem gives you the energy and angle for ball 2. You should be able to resolve ball 2's velocity into components and use the conservation of momentum to find ball 1's velocity components.
Does this make sense?

4. Jul 14, 2011

### azureth

What bacon stated is correct.Here you may only make use of the conservation of momentum along the x axis and the y axis

5. Jul 14, 2011

### azureth

As for answer ,I guess bacon's is correct.They seems more accurate than those on your book.